5e(7e+1)=4(1-10e^2)

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Solution for 5e(7e+1)=4(1-10e^2) equation: 


Simplifying
5e(7e + 1) = 4(1 + -10e2)

Reorder the terms:
5e(1 + 7e) = 4(1 + -10e2)
(1 * 5e + 7e * 5e) = 4(1 + -10e2)
(5e + 35e2) = 4(1 + -10e2)
5e + 35e2 = (1 * 4 + -10e2 * 4)
5e + 35e2 = (4 + -40e2)

Solving
5e + 35e2 = 4 + -40e2

Solving for variable 'e'.

Reorder the terms:
-4 + 5e + 35e2 + 40e2 = 4 + -40e2 + -4 + 40e2

Combine like terms: 35e2 + 40e2 = 75e2
-4 + 5e + 75e2 = 4 + -40e2 + -4 + 40e2

Reorder the terms:
-4 + 5e + 75e2 = 4 + -4 + -40e2 + 40e2

Combine like terms: 4 + -4 = 0
-4 + 5e + 75e2 = 0 + -40e2 + 40e2
-4 + 5e + 75e2 = -40e2 + 40e2

Combine like terms: -40e2 + 40e2 = 0
-4 + 5e + 75e2 = 0

Factor a trinomial.
(-4 + -15e)(1 + -5e) = 0


Subproblem 1
Set the factor '(-4 + -15e)' equal to zero and attempt to solve:

Simplifying
-4 + -15e = 0

Solving
-4 + -15e = 0

Move all terms containing e to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + -15e = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -15e = 0 + 4
-15e = 0 + 4

Combine like terms: 0 + 4 = 4
-15e = 4

Divide each side by '-15'.
e = -0.2666666667

Simplifying
e = -0.2666666667

Subproblem 2
Set the factor '(1 + -5e)' equal to zero and attempt to solve:

Simplifying
1 + -5e = 0

Solving
1 + -5e = 0

Move all terms containing e to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -5e = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5e = 0 + -1
-5e = 0 + -1

Combine like terms: 0 + -1 = -1
-5e = -1

Divide each side by '-5'.
e = 0.2

Simplifying
e = 0.2
Solution
e = {-0.2666666667, 0.2}

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